Convex duality and the Skorokhod problem. I
type: Item
instance of: scholarly article
title: Convex duality and the Skorokhod problem. I
zbMATH Open document ID: 0944.60061
author: Paul Dupuis
author: Kavita Ramanan
publication date: 2000-09-13T00:00:00Z
review text: It is considered the following problem (Skorokhod problem): given a closed set \(G\subset {\mathbb{R}}^{n}\), and a set of unit vectors \(d(x)\) at each point \(x\) on the boundary of \(G\), and a path \(\psi\) taking values in \({\mathbb{R}}^{n}\), define a constrained version \(\varphi\) of \(\psi\), where the constraint mechanism acts along the direction \(d(\cdot)\) in such a way that \(\varphi\) is keeping in \(G\). The main attention is paid to the case of \(G\) being a convex polyhedron. Using convex duality the authors reformulate the geometric type solvability conditions developed earlier by one of them in order to construct Skorokhod map associated with the Skorokhod problem and to verify the Lipschitz continuity of the solution. [For part II see below].
reviewed by: Sergei V. Rogosin
Mathematics Subject Classification ID: 60G99
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 52B11
Mathematics Subject Classification ID: 60K25
zbMATH DE Number: 1398348
zbMATH Keywords: Skorokhod problem
zbMATH Keywords: constrained deterministic and stochastic processes
zbMATH Keywords: convex polyhedron
zbMATH Keywords: convex duality
zbMATH Keywords: Lipschitz continuity
MaRDI profile type: Publication
full work available at URL: s004400050269
OpenAlex ID: W4242344947
DOI: 10.1007/S004400050269
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 1398348